Question: Simplify the following expression: $ p = \dfrac{r - 3}{6r} + \dfrac{1}{8} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{r - 3}{6r} \times \dfrac{8}{8} = \dfrac{8r - 24}{48r} $ Multiply the second expression by $\dfrac{6r}{6r}$ $ \dfrac{1}{8} \times \dfrac{6r}{6r} = \dfrac{6r}{48r} $ Therefore $ p = \dfrac{8r - 24}{48r} + \dfrac{6r}{48r} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{8r - 24 + 6r}{48r} $ $p = \dfrac{14r - 24}{48r}$ Simplify the expression by dividing the numerator and denominator by 2: $p = \dfrac{7r - 12}{24r}$